As is shown in FIGS. 1A through 1D, the present invention relates to a toy (5) having three bobs (10), (11) and (12) on a string (20), with the end bobs (10) and (12) constrained at the ends (21) and (22) of the string (20), and the middle bob (11) having a throughbore (30) through which the string (20) passes, thereby allowing the middle bob (11) to slide along the string (20). The toy (5) may be operated by holding an end bob (12) and oscillating the hand (41) to produce, for instance, vertical orbits of the bobs (10) and (11), as is shown in the time sequence of FIGS. 1A through 1D. In addition, stable horizontal orbits and stable figure-eight type orbits, or irregular orbits, can be generated by holding an end bob (12) and oscillating the hand. Furthermore, given the combinatorics of possible orbital directions and holds and transitions between holds with one or both hands of one or more of the bobs (10), (11) and (12) and/or one or more sections of the string (20), a very large number of tricks and maneuvers may be performed.
As discussed in U.S. Pat. Nos. RE34208, 6,629,873 and 6,896,578 (which are incorporated herein by reference), a crucial aspect of the design of orbiting bob toys (5) where the middle bob (11) acts as a sliding focus/pivot point to the orbiting of an outer bob (12) is that the middle bob (11) has a low moment of inertia about axes perpendicular to the bore axis. A low moment of inertia insures that the middle bob (11) can rotate rapidly in response to torques on the middle bob (11) produced by the tension of the string (20) during the “string pass” of vertical orbits, i.e., the period where the orbiting end bob (12) is at the top of its orbit and passes by the string (20) between the held end bob (10) and the middle ball (11)) so that play feels smooth and the string (20) does not snag around the middle bob (11). For play to feel smooth, the middle bob (11) must complete a 180° rotation during the string pass in roughly 1/20th of a second.
A measure of the goodness of operation of the design of the middle bob (11) is a dimensionless goodness-of-operation ratio Φ given byΦ=(mh2/I)1/2  (1.1)where m is the mass of a bob (10), (11) or (12), h is the height of the throughbore through the middle bob (11), and I is the moment of inertia of the middle bob (11) about an axis of rotation in the equatorial plane of the middle bob (11). The moment of inertia I is given byI=∫ρr2dτ,  (1.2)where ρ is density, r is distance from the axis of rotation, dτ is an infinitesimal volume element, and the integration is performed over volume. When the middle bob (11) has a large goodness-of-operation ratio Φ, not only will snagging of the string (20) about the middle ball (11) be avoided, the orbits will have an attractive smooth, relaxing feel.
It should be noted that the dependence of moment of inertia I on the second power of the distance r results in a dramatic dependence on dimensions. The sensitivity to dimensions produced by the r2 weighting is exemplified by the fact that for a sphere of homogeneous mass of radius R, the inner half of a sphere (i.e., the region within a radius of R/2) contributes only about 3% to the total moment of inertia, while the outer half contributes about 97% to the total moment of inertia.
Maximization of the goodness-of-play ratio Φ has previously been accomplished in several ways. As discussed in U.S. Pat. No. RE34,208 and shown in FIG. 4 of that patent, one maximization method is to locate a metal weight in the central region of the bob, and provide an outside mantle of a low-density material. However, with this design the size of bobs is limited by material constraints. In versions produced by New Toy Classics of San Francisco, Calif., Tangent Toy Company of Sausalito, Calif., and Active People of Binningen, Switzerland, the central weight was made of the highest density, non-toxic, non-radioactive, non-precious metals, i.e., brass and steel, and the outer mantle was made of one of the most durable, low-density foams, i.e., integral-skin polyurethane foam. Brass has a specific gravity of roughly 8.5, steel has a specific gravity of roughly 7.9, and integral-skin polyurethane foam has a specific gravity of roughly 0.25. Due to the practical upper and lower limits in specific gravity of the components, the bobs (10), (11) and (12) have been limited to a diameter of less than 3.5 cm. In particular, each bob (10), (11) and (12) had a cylindrical brass weight with a height of 1.27 cm, width of 1.27 cm, and throughbore width of 0.32 cm, a mass mw of 12.5 g and a moment of inertia Iw of 2.98 g*cm2. And each bob (10), (11) and (12) had a substantially spherical polyurethane foam outer mantle with a diameter of 3.3 cm and height of 2.7 cm, throughbore sections which are substantially conical, a mass mm of 3.8 g, and a moment of inertia Iw of 4.15 g*cm2. The goodness-of-operation ratio Φ is therefore [(mw+mm) h2/(Iw+Im)]1/2=[(12.5+3.8)*2.72/(2.98+4.15)]1/2≅4.1. It should further be noted that a sufficiently soft foam is difficult to achieve with integral-skin polyurethane foam. Furthermore, the process of producing integral-skin polyurethane foam is very sensitive to temperature and humidity, and there is often considerable variability in softness in the course of even a single production run.
Another approach has been to produce bobs with liquid-filled bladders. As described in U.S. Pat. No. 6,896,578, fluid flows in the bladder produce a lowered dynamic moment of inertia. The liquid used is predominantly water since, of economical, non-toxic liquids, water has a particularly low viscosity. However, the size of the bobs (10), (11) and (12) has been limited to a diameter of less than 3.6 cm due to the specific gravity of water of 1 g/cc contributing significantly to weight as size increases.
It should be noted that the diameters of the above-described orbiting bob toys are substantially smaller than the diameter of bobs, chassis, or bodies of other common skill toys. For instance, the balls of Kendama toys, the bobs of poi toys, and the bodies of yo-yos generally have a diameter of about 5 cm or greater. These larger diameters provide the important advantages of allowing the bobs/bodies to be more easily grasped and more easily visible to the player and any audience.
Furthermore, with regards to the toys taught in U.S. Pat. Nos. RE34208, 6,629,873 and 6,896,578, in cross-section on a plane along the bore axis (i.e., in “profile”) the throughbore has sections which in profile are substantially linear or convex. The advantage of linear or convex sections is that they can create contact, and therefore distribute pressure, between the string and the bore section along an extended length of the string and the bore section. This is particularly advantageous when the linear or convex section is made of a compressible material, such as foam, since the degree to which the string digs into the bore material is reduced, thereby reducing sliding friction. It should also be noted that because the string may slide over the bore transversely as well as longitudinally, a surface of cylindrical symmetry is required to avoid the string catching on protrusions in any region where the string makes contact with the throughbore.
Objects of the present invention for an orbiting bob toy include:
providing a middle bob with a low moment of inertia,
increasing the size of the bobs, particularly to be large enough to be easily visible and graspable,
providing a throughbore contour which reduces moment of inertia and takes advantage of forces produced by the string to increase torques,
providing a throughbore surface with non-cylindrical symmetry, particularly for the purpose of reducing moment of inertia,
maximizing a goodness-of-operation ratio,
providing bobs that are soft so impacts of bobs with the player cause minimal discomfort,
providing bobs which have a mantle which includes low-density granules, and
providing an orbiting bob toy having a wide variety of surface designs.